I don't know about drilling and greasing. I would ask a wheel shop to check them for you. They could be worn, and greasing them won't necessarily make them safe again.
With a few basic large tools, you should be able to bust the suspension apart and replace. The ball joints for my Durango were like $50 for the heavy greasable ones. I "borrowed" a ball joint tool from one of the big name parts stores in exchange for buying the parts there. Only have to be careful about breaking bolts off and having to drill them out.
I also thought I had a squeaky suspension on that durango, but it turned out to be the fluid in the rear diff needed replaced. There are many things that could start squeaking. I still think the best bet is to take it in and have a shop look it over. The place down the road from me will perform a basic inspection for free. You might get that lucky.